Two new types of quantum states are constructed by applying the operator s(ξ)=exp(ξ^*ab-ξa^†b^†) on the two-mode even and odd coherent states. The mathematical and quantum statistical properties of such states are investigated. Various nonclassical features of these states, such as squeezing properties, the inter-mode photon bunching, and the violation of Cauchy-Schwarz inequality, are discussed. The Wigner function in these states are studied in detail.